"We have again taken to the streets. We are striking, we are resisting the slaughtering of our rights," Ilias Vrettakos, a vice president of the main public sector union, said.
Earlier, authorities tried to prevent hundreds of Communist-affiliated strikers stopping tourists boarding ships bound for the Greek islands.
The recurring labour unrest has cost Greece booking many cancellations and millions of euros in damages at a time when the debt-hit nation is struggling to maximise its revenues and revive its economy.
"Greek islanders are counting on the next month for funds," Manolis Galanakis, deputy chairman of Greek coastal shipping associations, told Mega television.
Barnaby Phillips, Al Jazeera's correspondent in Athens, said tear gas had been used on the crowds at the port.
"There were some quite dramatic scenes this morning with tear gas being fired by the police, dispersing trade unions, many tourists running away very frightened," he said.
"Precisely not the kind of images Greece needs as it tries to get the tourist industry reinvigorated, after it got off to a slow start after all the trouble throughout the spring."
Local media, schools, banks and municipal offices have been shut down during the strike - the fifth walkout by major public and private sector unions this year.
Hospitals operated with emergency staff and public offices were mostly closed.
About 60 domestic flights were also cancelled but international flights were unaffected.
Many Greeks do not believe the government's financial measures will yield a positive outcome.
"These measures will not help. They will only lead to deeper recession and poverty," Despina Spanou, board member of the public sector union ADEDY, said.
"Workers will clearly answer the government and this reform which abolishes social security."
However, the government insists the spending cuts are vital.
"We deeply believe what we are doing is in the interests of the Greek people," George Petalotis, a government spokesman, said.
The southern European country avoided bankruptcy last month after receiving the first instalment payment of a $136bn emergency loan package from the European Union and the International Monetary Fund.
In return, Athens has passed severe austerity measures, including cutting pensions and salaries and raising consumer taxes.